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The Fibonacci Series

The Fibonacci series is an infinite sequence of numbers in which each number after the first two is the sum of the preceding two numbers.

The series has many fascinating properties. For example, for all integral values of n:

R(n) x R(n) + R(n+1) x R(n+1) = R(2n+1)

A more complicated relationship which holds true for all integral values of n, m and t is:

R(n) x R(m+t) - R(m) x R(n+t) = (-1)m x R(n-m) x R(t)

The series is related to many other mathematical concepts, including the following:

  • the Golden Section
  • sin 18 degrees
  • the logarithmic spiral
  • the regular pentagon
  • Pascal's triangle
  • Penrose tiling

However, there is no reason to think that the Fibonacci numbers can be used to make accurate forecasts of the stockmarket.


   n              R(n)

   0                0
   1                1
   2                1
   3                2
   4                3
   5                5
   6                8
   7               13
   8               21
   9               34
  10               55
  11               89
  12              144
  13              233
  14              377
  15              610
  16              987
  17            1,597
  18            2,584
  19            4,181
  20            6,765
  21           10,946
  22           17,711
  23           28,657
  24           46,368
  25           75,025
  26          121,393
  27          196,418
  28          317,811
  29          514,229
  30          832,040
  31        1,346,269
  32        2,178,309
  33        3,524,578
  34        5,702,887
  35        9,227,465
  36       14,930,352
  37       24,157,817
  38       39,088,169
  39       63,245,986
  40      102,334,155
  41      165,580,141
  42      267,914,296
  43      433,494,437
  44      701,408,733
  45    1,134,903,170
  46    1,836,311,903
  47    2,971,215,073
  48    4,807,526,976
  49    7,778,742,049
  50   12,586,269,025
  51   20,365,011,074
  52   32,951,280,099
  53   53,316,291,173
  54   86,267,571,272
  55  139,583,862,445
  56  225,851,433,717
  57  365,435,296,162
  58  591,286,729,879

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This page http://users.bigpond.net.au/renton/903.htm was last updated on 2003-11-02